How to Calculate Search Scores and Rankings for Hybrid Searches

[nohanaga]

Hi team, I am wondering how search scores and rankings are calculated for hybrid searches. I did a search with keyword search(top=10) and vector search(vector.k=10) and got the following ranking. RRFscore(d) = Σ (1 / (k + rank_d_i)) with constant k = 59.

1, Simple Vector Search Result

FileName	Vector-Rank	Vector-RRF
A.txt	2	1/(k+2)=0.016393443
B.txt	1	1/(k+1)=0.016666667
C.txt	3	1/(k+3)=0.016129032

2, Simple Keyword Search Result

FileName	Keyword-Rank	Keyword-RRF
A.txt	8	1/(k+8)=0.014925373
B.txt	10	1/(k+10)=0.014492754
C.txt	None	1/(k+?)=None

3, Σ RRF

FileName	calclated-RRF	displayed-RRF
A.txt	1/(k+2)+1/(k+8)=0.031318816	≈0.03131881356239319
B.txt	1/(k+1)+1/(k+10)=0.031159420	≈0.031159421429038048
C.txt	1/(k+3)=0.016129032	≠0.029286926612257957

Question 1. The docs describe k= like 60, but my calculation seems to be 59, how much is it actually?

Question 2. "C.txt" was not found in the Simple Keyword Search (top=10) results. How is the RRF calculated in this case? My guess is that internally a larger value than I specified in my top query is specified and its ranking is calculated.